Reed pointed out good things his administration did during a sometimes testy exchange with Carol Costello on "CNN Newsroom on Wednesday Morning."

"We got a million people out of the city," Reed said. "We have not had any fatalities. We cleared the way of all of our hospitals, all of our police stations."

Costello cut in to say, "Well, I heard this from public officials before, 'We didn't have any fatalities,' but that was just by the grace of God. There were a thousand traffic accidents. People got out of their cars on icy roadways in frigid conditions to walk home."

He told Costello the road treatment has been better than in January 2011, when "the city was closed for two to three days" because of a winter storm.

"The city didn't even have snow equipment in the last storm," Reed said, later adding that it had "four pieces of equipment" in 2011. Now, he said, besides the sand- and salt-spreaders and snowplows, the city has a crew that has "been working nonstop in 12-hour shifts."

At the news conference, Reed said 791 vehicle accidents -- "14 with injuries" -- were reported in the city since Tuesday's snowfall. He said city firefighters have supported 115 people, including stranded motorists.

Asked what he wanted to say to parents of children who stayed in schools overnight after Tuesday's snowfall, he said: "What I want to say to them is hold off on trying to get to them. What I can assure (you of) is they are safe."

He added: "The safest place for them was in the school system. ... I know it is very tough, but we're going to make sure we're going to get the roads open. ... But right now, we (need people to stay off the roads)."